%I A113308
%S A113308 1,1,1,2,1,3,1,4,2,5,1,8,1,7,4,10,1,13,1,15,6,11,1,27,2,13,8,28,1,27,1,
%T A113308 36,10,17,4,62,1,19,12,59,1,47,1,66,19,23,1,118,2,31,16,91,1,78,8,117,
%U A113308 18,29,1,193,1,31,26,159,10,115,1,153,22,51,1,320,1,37,35,190,6,161,1
%N A113308 a(n) = the number of finite sequences of positive integers {b(k)} where 
               (product b(k))* (sum b(k)) = n. Different orderings of the same integers 
               are counted separately.
%C A113308 Sequence's terms calculated by "Max".
%H A113308 Leroy Quet, <a href="http://www.prism-of-spirals.net/">Home Page</a> 
               (listed in lieu of email address)
%F A113308 a(n)=1 if n=1 or is a prime, a(2)=2 if n is the square of a prime. (Robert 
               G. Wilson v)
%e A113308 6 = 1*1*1*1*1*1*(1+1+1+1+1+1) = 1*2*(1+2) = 2*1*(2+1). So a(6) = 3.
%t A113308 (* first do *) Needs["DiscreteMath`Combinatorica`"] ( then *) t = Table[1, 
               {80}]; Do[k = 1; lmt = PartitionsP@n; p = Partitions@n; While[k < 
               lmt, a = Plus @@ p[[k]]*Times @@ p[[k]]; If[a < 81, t[[a]] += Length@ 
               Permutations@ p[[k]]]; k++ ], {n, 40}]; t (from Robert G. Wilson 
               v (rgwv(at)rgwv.com), May 03 2006)
%Y A113308 Cf. A113309.
%Y A113308 Sequence in context: A055440 A101279 A064576 this_sequence A143862 A115118 
               A115121
%Y A113308 Adjacent sequences: A113305 A113306 A113307 this_sequence A113309 A113310 
               A113311
%K A113308 nonn
%O A113308 1,4
%A A113308 Leroy Quet Oct 25 2005